diff --git a/slides/cours_21.md b/slides/cours_21.md
index 300abae67cf6798cedba2fc1a2fffccb539c087f..761f0e655b21602eee433f482f5e036209a09c47 100644
--- a/slides/cours_21.md
+++ b/slides/cours_21.md
@@ -273,6 +273,8 @@ rien moyenne(arbre) {
 
 # La compression avec pertes
 
+\footnotesize
+
 ## Pseudo-code (5min, matrix)
 
 . . .
diff --git a/slides/cours_22.md b/slides/cours_22.md
new file mode 100644
index 0000000000000000000000000000000000000000..47d8b8c3512a05f0e0563347a92117f1200990ac
--- /dev/null
+++ b/slides/cours_22.md
@@ -0,0 +1,366 @@
+---
+title: "B-Arbres"
+date: "2022-04-13"
+patat:
+  eval:
+    tai:
+      command: fish
+      fragment: false
+      replace: true
+    ccc:
+      command: fish
+      fragment: false
+      replace: true
+  images:
+    backend: auto
+---
+
+# Le cours précédent
+
+* Questions:
+
+
+
+# Les B-arbres
+
+## Problématique
+
+* Grands jeux de données (en 1970).
+* Stockage dans un arbre, mais l'arbre tiens pas en mémoire.
+* Regrouper les sous-arbres en **pages** qui tiennent en mémoire.
+
+## Exemple
+
+* 100 noeuds par page et l'arbre comporte $10^6$ noeuds:
+    * Recherche B-arbre: $\log_{100}(10^6)=3$;
+    * Recherche ABR: $\log_2(10^6)=20$.
+* Si on doit lire depuis le disque: $10\mathrm{ms}$ par recherche+lecture:
+    * $30\mathrm{ms}$ (lecture beaucoup plus rapide que recherche) vs $200\mathrm{ms}=0.2\mathrm{s}$.
+
+## Remarques
+
+* On sait pas ce que veut dire `B`: Bayer, Boeing, Balanced?
+* Variante plus récente B+-arbres.
+
+# Les B-arbres
+
+## Illustration, arbre divisé en pages de 3 noeuds
+
+![Arbre divisé en pages de 3 noeuds](figs/barbres_page3.png)
+
+. . .
+
+## Utilisation
+
+* Bases de données (souvent très grandes donc sur le disque);
+* Système de fichier.
+
+# Les B-arbres
+
+## Avantages
+
+* Arbres moins profonds;
+* Diminue les opération de rééquilibrage;
+* Complexité toujours en $\log(N)$;
+
+. . .
+
+## Définition: B-arbre d'ordre $n$
+
+* Chaque page d'un arbre contient au plus $2\cdot n$ *clés*;
+* Chaque page (excepté la racine) contient au moins $n$ clés;
+* Chaque page qui contient $m$ clés contient soit:
+    * $0$ descendants;
+    * $m+1$ descendants.
+* Toutes les pages terminales apparaissent au même niveau.
+
+# Les B-arbres
+
+## Est-ce un B-arbre?
+
+![B-arbre d'ordre 2.](figs/barbres_exemple.png)
+
+. . .
+
+## Oui!
+
+* Dans chaque noeud les clés sont **triées**.
+* Chaque page contient au plus $n$ noeuds: check;
+* Chaque noeud avec $m$ clés a $m+1$ descendants;
+* Toutes les feuilles apparaissent au même niveau.
+
+# Les B-arbres
+
+## Exemple de recherche: trouver `32`
+
+![B-arbre d'ordre 2.](figs/barbres_exemple.png)
+ 
+. . .
+
+* Si `n` plus petit que la 1e clé ou plus grand que la dernière descendre.
+* Sinon parcourir (par bissection ou séquentiellement) jusqu'à trouver ou descendre entre 2 éléments.
+
+# Les B-arbres
+
+## La recherche de la clé `C` algorithme 
+
+0. En partant de la racine.
+1. Si on est dans une feuille:
+    * Si la `C` est dans une page, retourner la page;
+    * Sinon c'est perdu.
+2. Sinon:
+    * Tant que `C > page` passer à la page suivante
+    * Descendre
+
+# Les B-arbres
+
+## Disclaimer
+
+* Inspiration de <https://en.wikipedia.org/wiki/B-tree>
+
+## Exemples d'insertion: `1`
+
+![B-arbre d'ordre 1.](figs/barbres_1.svg)
+ 
+. . .
+
+* L'arbre est vide, on insère juste dans la première page.
+
+# Les B-arbres
+
+## Exemples d'insertion: `2`
+
+![B-arbre d'ordre 1. Nombre pages max = 2.](figs/barbres_2.svg)
+ 
+. . .
+
+* La première page est pas pleine, on insère dans l'ordre (après 1).
+
+# Les B-arbres
+
+## Exemples d'insertion: `3`
+
+![B-arbre d'ordre 1.](figs/barbres_2.svg){width=50%}
+
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `3`
+
+![B-arbre d'ordre 1. Nombre pages max = 2.](figs/barbres_3.svg){width=50%}
+ 
+. . .
+
+* La page est pleine, on crée deux enfants.
+* On choisit, `2`, la médiane de `1, 2, 3` et il est inséré à la racine.
+* `1` descend à gauche, `3` descend à droite.
+
+# Les B-arbres
+
+## Exemples d'insertion: `4`
+
+![B-arbre d'ordre 1.](figs/barbres_3.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `4`
+
+![B-arbre d'ordre 1. Nombre enfants 0 ou 2.](figs/barbres_4.svg){width=50%}
+ 
+. . .
+
+* On pourrait insérer à droite de `2`, mais... ça ferait 2 parents pour 2 enfants (mais `m` parents => `m+1` enfants ou `0`);
+* On descend à droite (`4 > 2`);
+* On insère à droite de `3`.
+
+# Les B-arbres
+
+## Exemples d'insertion: `5`
+
+![B-arbre d'ordre 1.](figs/barbres_4.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `5`
+
+![B-arbre d'ordre 2.](figs/barbres_5.svg)
+ 
+. . .
+
+* On descend à droite (on peut pas insérer à la racine comme pour `4`);
+* On dépasse la capacité de l'enfant droite;
+* `4`, médiane de `3, 4, 5`, remonte à la racine;
+* On crée un nouveau noeud à droite de `4`;
+* La règle `m => m+1` est ok.
+
+# Les B-arbres
+
+## Exemples d'insertion: `6`
+
+![B-arbre d'ordre 1.](figs/barbres_5.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `6`
+
+![B-arbre d'ordre 2.](figs/barbres_6.svg)
+ 
+. . .
+
+* `6 > 4` on descend à droite;
+* `6 > 5` et on a à la place à droite, on insère.
+
+# Les B-arbres
+
+## Exemples d'insertion: `7`
+
+![B-arbre d'ordre 1.](figs/barbres_6.svg){width=50%}
+ 
+* Comment on insère (1min de réflexion avant de donner une réponse!)?
+
+# Les B-arbres
+
+## Exemples d'insertion: `7`
+
+![B-arbre d'ordre 2.](figs/barbres_7.svg){width=50%}
+ 
+. . .
+
+* `7 > 4` on descend à droite;
+* `7 > 6` mais on a dépassé la capacité;
+* `6` est la médiane de `5, 6, 7`, remonte à la racine;
+* `5` reste à gauche, `7` à droite, mais `6` fait dépasser la capacité de la racine;
+* `4` est la médiane de `2, 4, 6`, `4` remonte, `2` reste à gauche, `6` à droite.
+
+# Les B-arbres
+
+## L'algorithme d'insertion
+
+0. Rechercher la feuille (la page a aucun enfant) où insérer;
+1. Si la page n'est pas pleine insérer dans l'ordre croissant.
+2. Si la page est pleine, on sépare la page en son milieu :
+    1. On trouve la médiane, `M`, de la page;
+    2. On met les éléments `< M` dans la page de gauche de `M` et les `> M` dans la page de droite de `M`;
+    3. `M` est insérée récursivement dans la page parent.
+
+# Les B-arbres
+
+## Exercice: insérer `22` dans l'arbre d'ordre 2 (3min matrix)
+
+![](figs/barbres_ex1.png)
+
+. . .
+
+![](figs/barbres_ex2.png)
+
+
+# Les B-arbres
+
+## Exercice: insérer `5, 45, 50` dans l'arbre d'ordre 2 (3min matrix)
+
+![](figs/barbres_ex2.png)
+
+. . .
+
+![](figs/barbres_ex3.png)
+
+# Les B-arbres
+
+## Exercice: insérer `32, 55, 60` dans l'arbre d'ordre 2 (3min matrix)
+
+![](figs/barbres_ex3.png)
+
+. . .
+
+![](figs/barbres_ex4.png)
+
+# Les B-arbres
+
+## Exercice: insérer `41` dans l'arbre d'ordre 2 (3min matrix)
+
+![](figs/barbres_ex4.png)
+
+. . .
+
+![](figs/barbres_ex5.png)
+
+# Les B-arbres
+
+## Exercice
+
+* Insérer 20, 40, 10, 30, 15, 35, 7, 26, 18, 22, 5, 42, 13, 46, 27, 8, 32, 38, 24, 45, 25, 2, 14, 28, 32, 41,
+* Dans un B-arbre d'ordre 2.
+
+# Les B-arbres
+
+## Structure de données
+
+* Chaque page a une contrainte de remplissage, par rapport à l'ordre de l'arbre;
+* Un noeud (page) est composé d'un tableau de clés/pointeurs vers les enfants;
+
+```
+P_0 | K_1 | P_1 | K_2 |  | P_i | K_{i+1} |  | P_{m-1} | K_m | P_m
+```
+
+* `P_0`, ..., `P_m` pointeurs vers enfants;
+* `K_1`, ..., `K_m` les clés.
+* Il y a `m+1` pointeurs mais `m` clés.
+* Comment faire pour gérer l'insertion?
+
+# Les B-arbres
+
+## Faire un dessin de la structure de données (3min matrix)?
+
+. . .
+
+![Strcture d'une page de B-arbre d'ordre 2.](figs/barbres_struct.png)
+
+
+# Les B-arbres
+
+## Pseudo-code structure de données (3min, matrix)?
+
+. . .
+
+```C
+struct page
+    int ordre, nb
+    element tab[2*ordre + 2]
+```
+
+```C
+struct element
+    int clé
+    page pg
+```
+
+# Les B-arbres
+
+
+
+# Les B-arbres
+
+## Structure de données en C (3min, matrix)
+
+. . .
+
+```C
+typedef struct _page {
+    int order, nb;
+    struct _element *tab;
+} page;
+```
+
+```C
+typedef struct element {
+    int key;
+    struct _page *pg;
+} element;
+```
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